2) Timezones pain killers

3) Project management

This category is tough. When it comes to planning, I personally like to keep
things simple. Trello or Github Project
Board provide a good
enough board with columns and cards. That’s it.

If you need more heavy stuff, Jira
seems to be the most popular choice.

Basecamp should be considered too. Beside project
organization, it has team organization, status updates and document storage.
Now, team org can be a spreadsheet in Google Docs, where it along with other
docs will be stored. The final choice is up to you of course.